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Abstract:

A piezoelectric substrate includes vibrating arms, a base portion to
which one end portion of each vibrating arm is connected, spindle
portions formed in the other end portion of each vibrating arm, formed to
have a large width, and having first groove portions formed therein, and
second groove portions that are formed along the resonator center line of
each vibrating arm, and flexure-torsional combined resonator is excited.
A piezoelectric resonator element has flexural resonator of
flexure-torsional combined resonator that is excited as its principal
resonator and sets the cutting angle of the piezoelectric substrate, the
widths and the depths of the first groove portion and the second groove
portion, and the thickness of the vibrating arm such that the
frequency-temperature characteristics represent third-order
characteristics with respect to the temperature.

Claims:

1. A piezoelectric resonator element comprising: a piezoelectric
substrate including at least a plurality of vibrating arms, a base
portion to which one end portion of each one of the vibrating arms is
connected, spindle portions that are connected to the other end portion
of each one of the vibrating arms and have a width larger than that of
the other end portion of each one of the vibrating arms, a first groove
portion that extends along a longitudinal direction of each one of the
vibrating arms on at least one of front and rear faces of the spindle
portion, and a second groove portion that is disposed on front and rear
faces of each one of the vibrating arms, wherein flexure-torsional
combined resonator of which frequency-temperature characteristics
represent third-order characteristics with respect to the temperature is
performed.

2. The piezoelectric resonator element according to claim 1, wherein the
base portion includes: a base portion main body that includes one end
connected to the one end portion of each one of the vibrating arms; a
connection portion that is connected to the other end located on a side
facing the one end; and a support arm that is connected through the
connection portion and extends to be separated from the base portion main
body.

3. The piezoelectric resonator element according to claim 1, wherein the
piezoelectric substrate is configured by a quartz crystal plate, and a
normal line of a principal face of the quartz crystal plate is inclined
by an angle within a range of 0 degree to -15 degrees with respect to an
optical axis of a quartz crystal in accordance with rotation of an
electric axis of the quartz crystal.

4. The piezoelectric resonator element according to claim 1, wherein the
first groove portion includes a plurality of grooves separately aligned
along the longitudinal direction.

5. The piezoelectric resonator element according to claim 1, wherein the
first groove portions extend from tip end edges of the spindle portions
to center portions of the spindle portions and are formed at positions,
which have line symmetry with respect to a resonator center line of the
vibrating arms, located on the front and rear faces of the spindle
portions.

6. The piezoelectric resonator element according to claim 1, wherein the
first groove portion is formed to be continuous from the second groove
portion, and tip end portions of the first groove portions extend up to
front end edges of the spindle portions and are formed at positions,
which are symmetrical to each other with respect to the resonator center
line, located on the front and rear faces of the spindle portions.

7. The piezoelectric resonator element according to claim 5, wherein a
width of at least a part of the first groove portion is formed to be
larger than that of the second groove portion.

8. The piezoelectric resonator element according to claim 1, wherein the
first groove portion is a bottomed first groove portion.

9. The piezoelectric resonator element according to claim 1, wherein the
first groove portion is a first groove portion having a notch shape.

10. A piezoelectric resonator comprising: the piezoelectric resonator
element according to claim 1; and an insulating substrate that carries
the piezoelectric resonator element.

11. A piezoelectric resonator comprising: the piezoelectric resonator
element according to claim 2; and an insulating substrate that carries
the piezoelectric resonator element.

12. A piezoelectric oscillator comprising: the piezoelectric resonator
element according to claim 1; an IC component that excites the
piezoelectric resonator element; and a package that seals the
piezoelectric resonator element in an air-tight manner and houses the IC
component.

13. A piezoelectric oscillator comprising: the piezoelectric resonator
element according to claim 2; an IC component that excites the
piezoelectric resonator element; and a package that seals the
piezoelectric resonator element in an air-tight manner and houses the IC
component.

14. A resonator gyro element comprising: the piezoelectric resonator
element according to claim 1, wherein the piezoelectric resonator element
includes a detecting vibrating arm that is connected to the base portion
and is used for detecting an angular velocity.

15. A resonator gyro element comprising: the piezoelectric resonator
element according to claim 2, wherein the piezoelectric resonator element
includes a detecting vibrating arm that is connected to the base portion
and is used for detecting an angular velocity.

16. A resonator gyro sensor comprising: the resonator gyro element
according to claim 14; and a package that houses the resonator gyro
element.

17. A resonator gyro sensor comprising: the resonator gyro element
according to claim 15; and a package that houses the resonator gyro
element.

18. An electronic apparatus comprising: the piezoelectric resonator
element according to claim 1.

19. An electronic apparatus comprising: the piezoelectric resonator
element according to claim 2.

Description:

BACKGROUND

[0001] 1. Technical Field

[0002] The present invention relates to a piezoelectric resonator element,
a resonator gyro element, and the like, and more particularly, to a
piezoelectric resonator element, a piezoelectric resonator, a
piezoelectric oscillator, a resonator gyro element, and a resonator gyro
sensor that are decreased in size and have improved frequency-temperature
characteristics and an electronic apparatus using them.

[0003] 2. Related Art

[0004] Generally, in a small-size information device such as a mobile
computer, a hard disk drive or a mobile communication device such as a
cellular phone, a piezoelectric device is widely used as a reference
frequency source. In accordance with the progress of decrease in size of
electronic apparatuses in which a piezoelectric device is mounted, a
further decrease in the size of the piezoelectric device has been
requested.

[0005] In JP-A-55-75326, a tuning fork type quartz crystal resonator is
disclosed which is cut out in the range of 0° to -15° at
the rotation of an electric axis (one of crystal axes) of quartz crystal.
The frequency-temperature characteristics of the flexural resonator mode
of the principal resonator of the quartz crystal resonator are enhanced
by approaching and combining the resonance frequencies fF and
fT of the flexural resonator mode and the torsional resonator mode
that are excited in the tuning fork type crystal quartz resonator.

[0006] Generally, the frequency-temperature characteristics Δf/f of
a quartz crystal resonator is represented by a polynomial with respect to
temperature T. However, for practical use, the frequency-temperature
characteristics are approximated as a cubic polynomial, and the
first-order coefficient to the third-order coefficient are denoted by
α, β, and γ. The frequency-temperature characteristics
TfF of the flexural resonator mode are influenced by the torsional
resonator mode and depend on the thickness h of a piezoelectric
substrate. The thickness h is set such that the first-order coefficient
α=0 for various cutting angles θ, and, additionally, the
cutting angle θ and the thickness h for which the second-order
coefficient β is zero are set from values acquired in advance
through calculation. Accordingly, the frequency-temperature
characteristics TfF depend only on the third-order coefficient
γ, and it is disclosed that a quartz crystal resonator having
satisfactory temperature characteristics is acquired.

[0007] In addition, in JP-A-2004-282230, a tuning fork type piezoelectric
resonator is disclosed in which an expansion portion wider than a
vibrating arm is disposed in each tip end portion of a plurality of
vibrating arms that are parallel to one another. It has been written
therein that the expansion portion has a bottomed hole, and a material
having a specific gravity higher than that of a piezoelectric material is
filled in the bottomed hole so as to serve as a spindle, whereby the
miniaturization of the tuning fork type piezoelectric resonator is
achieved.

[0008] Furthermore, in JP-A-2010-2430, a resonator gyro element is
disclosed. The resonator gyro element includes: a base portion; one pair
of detection vibrating arms that extend from the base portion to both
sides in a linear shape; one pair of connecting arms extending from the
base portion to both sides in directions perpendicular to the detection
vibrating arms; and one pair of driving vibrating arms extending from the
tip end portions of the connecting arms to both sides to be perpendicular
to the tip end portions. In addition, two pairs of beams extending from
the base portion along the detecting arms and one pair of support
portions to which the beams extending in the same direction are connected
are included in the same plane, and the support portions are configured
to be arranged on the outer side of the detection vibrating arms in
directions in which the detection vibrating arms extend and between the
driving vibrating arms.

[0009] However, according to the tuning fork type piezoelectric resonator,
which is disclosed in JP-A-55-75326, of which the frequency-temperature
characteristics are improved by approaching and combining the frequencies
of the flexural resonator mode and the torsional resonator mode, there is
a problem in that it is difficult to decrease the size thereof.

[0010] In addition, according to the tuning fork type piezoelectric
resonator disclosed in JP-A-2004-282230, although the size thereof can be
decreased by forming the spindle portion in the tip end portion of the
vibrating arm, the frequency-temperature characteristics have
second-order characteristics, and there is a problem in the frequency
stability.

[0011] Furthermore, according to the resonator gyro element disclosed in
JP-A-2010-2430, there is a problem in that the sensitivity for the
angular velocity changes in accordance with a change in the temperature.

SUMMARY

[0012] An advantage of some aspects of the invention is that it provides a
piezoelectric resonator element, a piezoelectric resonator, a
piezoelectric oscillator, and a resonator gyro sensor that are decreased
in size and have improved frequency-temperature characteristics and an
electronic apparatus using them.

Application Example 1

[0013] This application example is directed to a piezoelectric resonator
element including: a piezoelectric substrate including at least a
plurality of vibrating arms, a base portion to which one end portion of
each one of the vibrating arms is connected, spindle portions that are
connected to the other end portion of each one of the vibrating arms and
have a width larger than that of the other end portion of each one of the
vibrating arms, a first groove portion that extends along a longitudinal
direction of each one of the vibrating arms on at least one of front and
rear faces of the spindle portion, and a second groove portion that is
disposed on front and rear faces of each one of the vibrating arms; and
excitation electrodes that are formed on the front and rear faces of the
spindle portion and the front and rear faces and both side faces of each
vibrating arm including the inside of each second groove portion and are
electrically connected to a plurality of electrode pads disposed in the
base portion. In addition, the piezoelectric resonator element performs
flexure-torsional combined resonator, and the frequency-temperature
characteristics of the piezoelectric resonator element represent
third-order characteristics with respect to the temperature.

[0014] Each spindle portion is formed in the tip end portion of each
vibrating arm of the tuning fork type piezoelectric resonator element,
the first groove portion extending in a linear shape along the
longitudinal direction of the vibrating arm on the front and rear faces
of the spindle portion is formed, and the second groove portion is formed
on the front and rear faces along the resonator center line of each
vibrating arm. By configuring as such, the flexural resonator and the
torsional resonator excited in the tuning fork type piezoelectric
resonator element can approach each other so as to be combined together.
The frequency-temperature characteristics of the flexural resonator of
the flexure-torsional combined resonator have third-order characteristics
with respect to the temperature, and there is an advantage of acquiring
the piezoelectric resonator element that has superior temperature
characteristics and has a small size.

Application Example 2

[0015] This application example is directed to the piezoelectric resonator
element according to Application Example 1, wherein the base portion
includes: a base portion main body that includes one end connected to the
one end portion of each one of the vibrating arms; a connection portion
that is connected to the other end located on a side facing the one end
connected to the vibrating arms of the base portion main body; and a
support arm that is connected through the connection portion and extends
to be separated from the base portion main body.

[0016] The base portion of the piezoelectric resonator element includes
the base portion main body, the connection portions, and the support arms
having an "L" shape and a reverse "L" shape, the end portions of the "L"
shape and the reverse "L" shape are connected to each other, and each
connection portion is configured to be connected to the center of one end
portion of the base portion main body through the connection portion.
Accordingly, the resonator energy leaking to the support arms from the
vibrating arms can be reduced, whereby the CI value is small, and the
impact resistance is improved. As a result, there is an advantage of
acquiring a piezoelectric resonator element having no problem of
frequency variations due to a damage, a destruction, or the like that is
caused by an impact.

Application Example 3

[0017] This application example is directed to the piezoelectric resonator
element according to Application Example 1 or 2, wherein the
piezoelectric substrate is configured by a quartz crystal plate, and a
normal line of a principal face of the quartz crystal plate is inclined
by an angle within a range of 0 degree to -15 degrees with respect to an
optical axis of a quartz crystal in accordance with rotation of an
electric axis of the quartz crystal.

[0018] The tuning fork type piezoelectric resonator element is configured
in which the cutting angle of the piezoelectric substrate is rotated
around the electric axis (the X axis) in the range of 0 degree to -15
degrees. By selecting the cutting angle as such, the first-order
coefficient and the second-order coefficient of the polynomial
representing the frequency-temperature characteristics of the
flexure-torsional combined resonator can be configured to be
approximately zero, and there is an advantage of acquiring a
piezoelectric resonator element having superior temperature
characteristics.

Application Example 4

[0019] This application example is directed to the piezoelectric resonator
element according to any one of Application Examples 1 to 3, wherein the
first groove portion includes a plurality of grooves separately aligned
along the longitudinal direction.

[0020] By configuring the piezoelectric resonator element in which the
first groove portions are formed as described above, the
frequency-temperature characteristics of the flexure resonator of the
flexure-torsional combined resonator have third-order characteristics
with respect to the temperature, and there are an advantage of acquiring
the piezoelectric resonator element having superior temperature
characteristics and an advantage of forming the lead electrodes that
electrically connect the excitation electrodes on the flat faces of the
spindle portions.

Application Example 5

[0021] This application example is directed to the piezoelectric resonator
element according to any one of Application Examples 1 to 3, wherein the
first groove portions extend from tip end edges of the spindle portions
to center portions of the spindle portions and are formed at positions,
which have line symmetry with respect to a resonator center line of the
vibrating arms, located on the front and rear faces of the spindle
portions.

[0022] By configuring the piezoelectric resonator element in which the
first groove portions are formed as described above, the
frequency-temperature characteristics of the principal resonator of the
flexure-torsional combined resonator have third-order characteristics
with respect to the temperature, and there are an advantage of improving
the temperature characteristics and an advantage of forming the lead
electrodes that electrically connect the excitation electrodes on the
flat faces of the spindle portions.

Application Example 6

[0023] This application example is directed to the piezoelectric resonator
element according to any one of Application Examples 1 to 3, wherein the
first groove portion is formed to be continuous from the second groove
portion, and tip end portions of the first groove portions extend up to
front end edges of the spindle portions and are formed at positions,
which are symmetrical to each other with respect to the resonator center
line, located on the front and rear faces of the spindle portions.

[0024] By configuring the piezoelectric resonator element in which the
first groove portions are formed as described above, the
frequency-temperature characteristics of the flexure resonator of the
flexure-torsional combined resonator have third-order characteristics
with respect to the temperature, and there are an advantage of improving
the temperature characteristics of the piezoelectric resonator element
and an advantage of easily forming masks used for forming the first and
second groove portions.

Application Example 7

[0025] This application example is directed to the piezoelectric resonator
element according to Application Example 5, wherein a width of at least a
part of the first groove portion is formed to be larger than that of the
second groove portion.

[0026] By configuring the piezoelectric resonator element in which the
first groove portions are formed as described above, the
frequency-temperature characteristics of the flexure resonator of the
flexure-torsional combined resonator have third-order characteristics
with respect to the temperature, and there are an advantage of improving
the temperature characteristics of the piezoelectric resonator element
and an advantage of easily combining the flexure resonator frequency and
the torsional resonator frequency by appropriately setting the width of
the first groove portions.

Application Example 8

[0027] This application example is directed to a piezoelectric resonator
including: the piezoelectric resonator element according to any one of
Application Examples 1 to 6; and an insulating substrate that carries the
piezoelectric resonator element.

[0028] The piezoelectric resonator is configured by allowing the flexural
resonator and torsional resonator excited in the tuning fork type
piezoelectric resonator element to approach each other and housing the
tuning fork type piezoelectric resonator element in which the
flexure-torsional combined resonator is excited in an insulating
substrate, whereby there is an advantage of acquiring a piezoelectric
resonator that has a high Q value due to its small size and has superior
frequency-temperature characteristics.

Application Example 9

[0029] This application example is directed to a piezoelectric oscillator
including: the piezoelectric resonator element according to any one of
Application Examples 1 to 6; an IC component that excites the
piezoelectric resonator element; and a package that seals the
piezoelectric resonator element in an air-tight manner and houses the IC
component.

[0030] The piezoelectric oscillator is configured so as to include: the
tuning fork type piezoelectric resonator element in which the flexural
resonator and the torsional resonator approach each other, and the
flexure-torsional combined resonator is excited; an IC component; and a
package that houses the tuning fork type piezoelectric resonator element
and the IC component, whereby there is an advantage of acquiring a
small-size piezoelectric oscillator having superior frequency-temperature
characteristics.

Application Example 10

[0031] This application example is directed to a resonator gyro element
including: the piezoelectric resonator element according to Application
Example 1, and the piezoelectric resonator element includes a detecting
vibrating arm that is connected to the base portion and is used for
detecting an angular velocity.

[0032] The resonator gyro element is configured in which each spindle
portion is formed in the tip end portion of each driving vibrating arm,
first groove portions extending in a linear shape along the longitudinal
direction of the vibrating arm are formed on the front and rear faces of
the spindle portion, and second groove portions are formed on the front
and rear faces along the resonator center line of each driving vibrating
arm. By configuring such a resonator gyro element, the
frequency-temperature characteristics of the flexural resonator that is
the principal resonator of the flexure-torsional combined resonator
excited in each driving vibrating arm represent third-order
characteristics with respect to the temperature, and accordingly, there
is an advantage of acquiring the resonator gyro element that has superior
temperature characteristics and a small size.

Application Example 11

[0033] This application example is directed to a resonator gyro sensor
including: the resonator gyro element according to Application Example
10; and a package that houses the resonator gyro element.

Application Example 12

[0034] This application example is directed to a piezoelectric resonator
element including: a piezoelectric substrate including a plurality of
vibrating arms, a base portion to which one end portion of each one of
the vibrating arms is connected, spindle portions that are formed to the
other end portion of each one of the vibrating arms and have a width
larger than that of each one of the vibrating arms, and groove portions
that are formed on the front and rear faces along the resonator center of
each vibrating arm; and excitation electrodes that are formed on both
faces of the spindle portion and the front and rear faces and the side
faces of each vibrating arm including the inside of each groove portion
and are electrically connected between a plurality of electrode pads
disposed in the base portion. Each spindle portion includes mass portions
having a heavy mass on both sides of the resonator center, the mass
portions are configured so as to be symmetrical with respect to the
resonator center, the flexural resonator of the flexure-torsional
combined resonator excited in the piezoelectric resonator element is
configured as its principal resonator, and the thickness of the
piezoelectric substrate, the cutting angle, and the widths and the depths
of the mass portion and the groove portion are set such that the
frequency-temperature characteristics represent third-order
characteristics with respect to the temperature.

[0035] According to the above-described piezoelectric resonator element
(tuning fork type piezoelectric resonator element), the spindle portion
is formed in the tip end portion of each vibrating arm, and the mass
portions having a heavy mass are arranged on both sides along the
resonator center in the spindle portion so as to be symmetrical. Further,
respective groove portions are formed on the front and rear faces along
the resonator center in the vibrating arms. By configuring as such, the
flexural resonator and the torsional resonator excited in the turning
fork type piezoelectric resonator element approach each other so as to be
combined together. By appropriately setting the thickness of the
piezoelectric substrate, the cutting angle, and the shapes of each mass
portion and each groove portion, the frequency-temperature
characteristics of the flexure resonator as the principal resonator of
the flexure-torsional combined resonator represent third-order
characteristics with respect to the temperature, and accordingly, there
is an advantage of acquiring the piezoelectric resonator element that has
superior temperature characteristics and has a small size.

Application Example 13

[0036] This application example is directed to the piezoelectric resonator
element according to Application Example 12, wherein the cutting angle of
the piezoelectric substrate is set to be in the range of 0 degree to -15
degrees in accordance with the rotation of the electric axis.

[0037] The piezoelectric resonator element (tuning fork type piezoelectric
resonator element) is configured in which the cutting angle of the
piezoelectric substrate is rotated in the range of 0 degree to -15
degrees in accordance with the rotation around the electric axis (the X
axis). By setting the cutting angle as such and appropriately setting the
thickness of the piezoelectric substrate and the like, the first-order
coefficient and the second-order coefficient of a polynomial representing
the frequency-temperature characteristics of the principal resonator of
the flexure-torsional combined resonator can be set to approximate zero,
and accordingly, there is an advantage of acquiring the piezoelectric
resonator element having superior temperature characteristics.

Application Example 14

[0038] This application example is directed to the piezoelectric resonator
element according to Application Example 12 or 13, wherein each spindle
portion forms a concave portion in the center portion of the tip end edge
by including notch portions that are symmetrical with respect to the
resonator center.

[0039] By disposing the notch portions that are symmetrical with respect
to the resonator center in the center portion of the tip end edge of each
spindle portion, the flexural resonator (tuning fork resonator) and the
torsional resonator excited in the piezoelectric resonator element can
approach each other so as to combined together. By appropriately setting
the parameters, there is an advantage of configuring the
frequency-temperature characteristics of the flexural resonator of the
flexure-torsional combined resonator to have third-order characteristics.

Application Example 15

[0040] This application example is directed to the piezoelectric resonator
element according to Application Example 14, wherein through holes that
are symmetrical with respect to the resonator center are formed within
the plane of the spindle portion closer to the vibrating arm than the
notch portion.

[0041] The spindle portions are reinforced by decreasing the size of the
notch portion, arranging the mass portions to be symmetrical with respect
to the resonator center on both sides thereof together with the through
holes, and arranging the bridging portion between both mass portions. At
the same time, the flexural resonator (tuning fork resonator) and the
torsional resonator can approach each other so as to be combined
together. Furthermore, by appropriately setting the parameters, there is
an advantage of configuring the frequency-temperature characteristics of
the flexural resonator of the flexure-torsional combined resonator to
represent third-order characteristics.

Application Example 16

[0042] This application example is directed to the piezoelectric resonator
element according to Application Example 12 or 14, wherein each spindle
portion includes through holes that are symmetrical with respect to the
resonator center in the center portion of the area.

[0043] By arranging the through hole in the center portion, while the
rigidity of the spindle portion is increased, the change in the frequency
of the flexural resonator slightly decreases. However, by slightly
increasing the area of the through hole, the decrease in the frequency
can be supplemented. Even in such a case, the frequencies of the flexural
resonator (tuning fork resonator) and the torsional resonator can
approach each other so as to be combined together. In addition, by
appropriately setting the parameters, there is an advantage of
configuring the frequency-temperature characteristics of the flexural
resonator of the flexure-torsional combined resonator to represent
third-order characteristics.

Application Example 17

[0044] This application example is directed to the piezoelectric resonator
element according to Application Example 12 or 13, wherein each spindle
portion includes a through hole that is symmetrical with respect to the
resonator center at the side end of the base portion, and the through
hole is connected to the groove portion of each vibrating arms.

[0045] By disposing the through hole at the side end of the base portion
of the spindle portion, although the change in the frequency of the
flexural resonator slightly decreases, by extending the groove portion of
the vibrating arm, the frequency of the torsional resonator decreases,
whereby two frequencies of the flexural resonator and the torsional
resonator can approach each other so as to be combined together. In
addition, by appropriately setting the parameters, there is an advantage
of configuring the frequency-temperature characteristics of the flexural
resonator of the flexure-torsional combined resonator to represent
third-order characteristics.

Application Example 18

[0046] This application example is directed to the piezoelectric resonator
element according to any one of Applications 12 to 17, wherein the base
portion includes a base portion main body, a connecting portion arranged
in the center portion of the other end edge of the base portion main body
that is located on a side opposite to the vibrating arm, and one pair of
left and right support arms that are connected through the connecting
portion and extend so as to be separated from the base portion main body.

[0047] The base portion of the piezoelectric resonator element (tuning
fork type piezoelectric resonator element) includes the base portion main
body, the connecting portion, the "L"-shaped support arm, and the reverse
"L"-shaped support arm. In the base portion, the end portions of the "L"
shape and the reverse "L" shape are connected together, and the
connection portion is configured to be connected to the center of one end
portion of the base portion main body through the connecting portion.
Accordingly, the resonator energy leaking to the support arms from the
vibrating arms can be reduced, whereby the CI value is small, and the
impact is alleviated by the structure of the base portion so as to
improve impact resistance. As a result, there is an advantage of
acquiring a piezoelectric resonator element having no problem of
frequency variations due to a damage, a destruction, or the like that is
caused by an impact.

Application Example 19

[0048] This application example is directed to a piezoelectric resonator
including: the piezoelectric resonator element according to any one of
Application Examples 12 to 18; and a package that houses the
piezoelectric resonator element.

[0049] The flexural resonator and the torsional resonator excited in the
above-described piezoelectric resonator element (tuning fork type
piezoelectric resonator element) are configured to approach each other,
and the tuning fork type piezoelectric resonator element in which the
flexure-torsional combined resonator is excited is housed in an
insulating substrate, whereby the piezoelectric resonator is configured.
As a result, there is an advantage of acquiring a piezoelectric resonator
that has a high Q value due to its small size and has superior shock
resistance and superior frequency-temperature characteristics.

Application Example 20

[0050] This application example is directed to a piezoelectric oscillator
including: the piezoelectric resonator element according to any one of
Application Examples 12 to 18; an IC component in which an oscillation
circuit that excites the piezoelectric resonator element is mounted; and
a package that seals the piezoelectric resonator element in an air-tight
manner and houses the IC component.

[0051] By configuring the piezoelectric oscillator that includes: the
piezoelectric resonator element (tuning fork type piezoelectric resonator
element) in which the flexural resonator and the torsional resonator are
approached each other the flexure-torsional combined resonator is
excited; the IC component that oscillates the piezoelectric resonator
element, and the package housing them, there is an advantage of acquiring
a piezoelectric oscillator that has a small size and superior
frequency-temperature characteristics.

Application Example 21

[0052] This application example is directed to a resonator gyro element
including: a base portion; one pair of detecting vibrating arms that
protrude from two end edges of the base portion, which face each other,
on the same line; one pair of connecting arms that protrude from the
other two end edges of the base portion, which face each other, on the
same line in a direction perpendicular to the detecting vibrating arms;
one pair of driving vibrating arms that protrude from the end portion of
each connecting arm in both directions perpendicular thereto; and
excitation electrodes that are formed in at least the one pair of
detecting vibrating arms and the one pair of driving vibrating arms and
are electrically connected between a plurality of electrode pads disposed
in the base portion. Each driving vibrating arm includes a groove portion
that extends in a linear shape along the longitudinal direction of each
vibrating arm on the front and rear faces and a spindle portion having a
width larger than that of each vibrating arm in the tip end portion. Each
spindle portion includes mass portions that are symmetrical with respect
to the resonator center on both sides thereof, the flexural resonator of
the flexure-torsional combined resonator excited in the driving vibrating
arm is configured as the principal resonator, and the cutting angle of
the substrate of the resonator gyro element and the widths and the depths
of the mass portion and the groove portion are set such that the
frequency-temperature characteristics represent third-order
characteristics with respect to the temperature.

[0053] The resonator gyro element is configured in which each spindle
portion is formed in the tip end portion of each driving vibrating arm, a
notch portion is formed to be symmetrical with respect to the resonator
center along the longitudinal direction of the vibrating arm in the
spindle portion, and groove portions are formed on the front and rear
faces of each driving vibrating arm along the resonator center. By
configuring as such, the frequency-temperature characteristics of the
flexural resonator that is the principal resonator of the
flexure-torsional combined resonator excited in each driving vibrating
arm represent third-order characteristics with respect to the
temperature, and accordingly, there is an advantage of acquiring a
resonator gyro element having superior temperature characteristics and
having a small size.

Application Example 22

[0054] This application example is directed to a resonator gyro sensor
including the resonator gyro element according to Application Example 21
and a package that houses the resonator gyro element.

[0055] By configuring the resonator gyro sensor by housing the resonator
gyro element in the package, the frequency-temperature characteristics of
the principal resonator of the flexure-torsional combined resonator
excited in each driving vibrating arm are improved, and, by arranging the
spindle portion, there is an advantage of acquiring a small-size
resonator gyro sensor.

Application Example 23

[0056] This application example is directed to an electronic apparatus
that includes: the piezoelectric resonator according to Application
Example 19 or the resonator gyro sensor according to Application Example
22.

[0057] By configuring an electronic apparatus including the
above-described piezoelectric resonator, there is an advantage of
improving the stability of the frequency source of the electronic
apparatus. In addition, by configuring an electronic apparatus including
the above-described resonator gyro sensor, there is an advantage of
reducing the change in the sensitivity of the angular velocity for the
temperature.

[0058] By configuring the resonator gyro sensor as above, the
frequency-temperature characteristics of the principal resonator of the
flexure-torsional combined resonator excited in each driving vibrating
arm are improved, and, by arranging the spindle portion, there is an
advantage of acquiring a small-size resonator gyro sensor.

Application Example 24

[0059] This application example is directed to an electronic apparatus
that includes: the piezoelectric resonator according to Application
Example 8 or the resonator gyro sensor according to Application Example
11.

[0060] By configuring an electronic apparatus including the piezoelectric
resonator as above, there is an advantage of improving the stability of
the frequency source of the electronic apparatus. In addition, by
configuring an electronic apparatus including the above-described
resonator gyro sensor, there is an advantage of reducing the change in
the sensitivity of the angular velocity for the temperature.

BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The invention will be described with reference to the accompanying
drawings, wherein like numbers reference like elements.

[0062]FIG. 1A is a schematic plan view showing the structure of a
piezoelectric resonator element according to an embodiment of the
invention, and FIG. 1B is a cross-sectional view of a vibrating arm.

[0063]FIG. 2 is a cross-sectional view of a spindle portion disposed in a
tip end portion of the vibrating arm.

[0065]FIG. 4A is an explanatory diagram showing changes in the
frequencies of the flexural resonator and the torsional resonator in a
case where a groove is formed in the tip end portion of a beam, FIG. 4B
is an explanatory diagram showing changes in the frequencies of the
flexural resonator and the torsional resonator in a case where a groove
is formed in a center portion of the beam, and FIG. 4C is an explanatory
diagram showing changes in the frequencies of the flexural resonator and
the torsional resonator in a case where the plate thickness of the beam
is changed.

[0066] FIGS. 5A and 5B are plan views in a case where concave portions are
formed on the front and rear faces of the spindle portion, and FIG. 5C is
a plan view in a case where grooves are formed on the front and rear
faces of the tip end portion of the spindle portion.

[0067]FIG. 6 is a diagram showing the resonance frequencies of the
flexural resonator and the torsional resonator and a resonance frequency
difference (Δf) corresponding to each of the piezoelectric
resonator elements shown in FIGS. 5A-5C.

[0068]FIG. 7A is a diagram showing the frequency-temperature
characteristics of the tuning fork resonator (flexural resonator), FIG.
7B is a diagram showing the frequency-temperature characteristics of the
torsional resonator, and FIG. 7C is a diagram showing the
frequency-temperature characteristics of the flexure-torsional combined
resonator.

[0069]FIG. 8 is a diagram showing a combination of the flexural resonator
and the torsional resonator in a case where the plate thickness of the
vibrating arm is changed.

[0070]FIG. 9A is a diagram showing the relation among the plate
thickness, the first-order coefficients, and the second-order
coefficients of the flexural resonator and the torsional resonator in the
flexure-torsional combined resonator, and FIG. 9B is an enlarged diagram
of a main portion thereof.

[0071]FIG. 10 is a cross-sectional view of a piezoelectric resonator
using the flexure-torsional combined resonator.

[0072]FIG. 11 is a cross-sectional view of a piezoelectric oscillator.

[0073]FIG. 12A is a plan view of a resonator gyro sensor, FIG. 12B is a
cross-sectional view thereof, and FIG. 12C is a schematic diagram
illustrating the operation thereof.

[0075]FIG. 14A is a schematic plan view showing the structure of a
piezoelectric resonator element according to another embodiment of the
invention, and FIG. 14B is a cross-sectional view of a vibrating arm.

[0076]FIG. 15 is a plan view showing a modified example of a spindle
portion that is connected to the tip end portion of the vibrating arm.

[0077]FIG. 16 is a plan view showing a modified example of the spindle
portion.

[0078]FIG. 17 is a plan view showing a modified example of the spindle
portion.

[0079] FIGS. 18A to 18E are plan views of a notch portion and a through
hole formed in the spindle portion, and FIG. 18F is a plan view of a
groove portion having the same area as that of the notch portion.

[0080]FIG. 19 is a diagram showing the frequencies of the flexural
resonator and the torsional resonator excited in a tuning fork type
piezoelectric resonator element having a notch portion in the shape shown
in FIG. 18B and a tuning fork type piezoelectric resonator element having
a groove portion that has the same area as that of the notch portion and
a frequency difference thereof.

[0081]FIG. 20 is a diagram showing the frequencies of the flexural
resonator and the torsional resonator excited to a tuning fork type
piezoelectric resonator element having a through hole in the shape shown
in FIG. 18c and a tuning fork type piezoelectric resonator element having
a groove portion that has the same area as that of the through hole and a
frequency difference thereof.

[0082]FIG. 21 is a diagram showing the frequencies of the flexural
resonator and the torsional resonator excited to a tuning fork type
piezoelectric resonator element having a notch portion and a through hole
in the shape shown in FIG. 18D and a tuning fork type piezoelectric
resonator element having a groove portion that has the same area as that
of the notch portion and the through hole and a frequency difference
thereof.

[0083]FIG. 22 is a diagram showing the frequencies of the flexural
resonator and the torsional resonator excited to a tuning fork type
piezoelectric resonator element having a fine through hole and a groove
portion connected thereto in the shape shown in FIG. 18E and a tuning
fork type piezoelectric resonator element having a groove portion that
has the same area as that of the fine through hole and the groove portion
connected thereto and a frequency difference thereof.

[0084]FIG. 23 is a diagram showing the frequencies of the flexural
resonator and the torsional resonator excited to a tuning fork type
piezoelectric resonator element having a spindle portion in the shapes
shown in FIGS. 18B to 18E and a frequency difference thereof.

[0085]FIG. 24 is a diagram showing resonator leakages in a tuning fork
type piezoelectric resonator element having only a base portion main body
and a tuning fork type resonator element having a base portion including
a support arm, which are acquired through simulation.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0086] Hereinafter, embodiments of the invention will be described in
detail with reference to the drawings. FIG. 1A is a schematic plan view
showing the structure of a piezoelectric resonator element (tuning fork
type quartz crystal element) 1 according to an embodiment of the
invention. The piezoelectric resonator element 1 includes a piezoelectric
substrate 7 that has a flat plate shape and thin-film electrodes 25 that
are formed on the front and rear faces and the side face of the
piezoelectric substrate 7.

[0087] The piezoelectric substrate 7, as shown in FIG. 1A, includes: a
plurality of (two in this example) vibrating arms 15a and 15b, which have
a narrow band shape, extending side by side (in parallel with each other)
in a linear shape; a base portion 10 that connects one end portions (base
end portions) of the vibrating arms 15a and 15b; spindle portions 20a and
20b that are integrally formed so as to be connected to the other end
portions (tip end portions) of the vibrating arms 15a and 15b and are
wider than the width of the other end portions of the vibrating arms 15a
and 15b; and second groove portions 17a (17b) and 18a (18b) formed on the
front and rear faces along the resonator center line C of the vibrating
arms 15a and 15b.

[0088] The spindle portions 20a and 20b include bottomed first groove
portions 22a (22b) and 24a (24b) that extend in a linear shape along the
longitudinal direction (a direction extending along a segment joining one
end portion and the other end portion of the vibrating arm) of the
vibrating arms 15a and 15b on at least one (both faces in this example)
of the front and rear faces along the resonator center line C. In FIGS. 2
and 3A to 3C, reference numerals 22b and 24b represent the first groove
portions formed on the rear face of the spindle portions 20a and 20b.

[0089] Here, the resonator center line C is a line that passes through the
center of gravity of the vibrating arm and extends in the longitudinal
direction of the vibrating arm.

[0090] The thin film electrode 25 shown in FIG. 1B includes front and rear
faces of the spindle portions 20a and 20b, first groove portions 22a,
22b, 24a, and 24b, and excitation electrodes 30, 32, 34, and 36 that are,
as shown in FIG. 1B, formed on the front and rear faces and the side
faces of the vibrating arms 15a and 15b including the insides of the
second groove portions 17a (17b) and 18a (18b) and are electrically
connected between a plurality of electrode pads (not shown in the figure)
disposed in the base portion 10 through lead electrodes (not shown in the
figure). The thin film electrode 25 is formed inside a vacuum device by
using a deposition method or a sputtering method. In addition, in a case
where the function of the spindle portions 20a and 20b is achieved by
only attaching high-density metal such as gold Au to the inside of the
first groove portions 22a, 22b, 24a, and 24b, the electrodes do not
necessarily need to be formed on the flat surface of the spindle portions
20a and 20b.

[0091] In order to decrease resonator leakage and improve shock
resistance, the base portion 10 shown in FIG. 1A includes: a base portion
main body 12a; a narrow connection portion 12d disposed in the other end
edge center portion (the other end located on a side facing one end
connected to the vibrating arm) of the base portion main body 12a that is
located on a side opposite to the vibrating arms 15a and 15b; and one
pair of left and right support arms 12b and 12c that extend in the
longitudinal direction with the vibrating arms 15a and 15b interposed
therebetween from the front side extending along the widthwise direction
in a state in which the support arms are connected through the connection
portion 12d and are separated from the base portion main body 12a. In
other words, in the example of the base portion, the base end portion of
the support arm 12b having an "L" shape and the base end portion of the
support arm 12c having a reverse "L" shape are connected together, the
connection portion is connected to one end edge center of the base
portion main body 12a through the connection portion 12d so as to form
the shape of "U", and the base end portions of the vibrating arms 15a and
15b are connected to the other end edge of the base portion main body
12a.

[0092] In the embodiment shown in FIGS. 1A and 1B, although the base
portion 10 has been described to include the base portion main body 12a,
the connection portion 12d, and one pair of the left and right support
arms 12b and 12c, only the base portion main body 12a may be included.

[0093] In addition, the vibrating arms 15a and 15b extend from the end
portion of the base portion main body 12a so as to be parallel to each
other with a gap interposed therebetween, and, in the tip end portions of
the vibrating arms 15a and 15b, spindle portions 20a and 20b wider than
the width of the other end portions of the vibrating arms 15a and 15b are
disposed so as to be integrated.

[0094] As the piezoelectric substrate 7, for example, in a case where a
quartz crystal substrate is used, a substrate that is acquired by cutting
out a Z substrate (a substrate cut out so as to be perpendicular to the
optical axis (Z axis)) by rotating the electric axis (X axis) by
0° to -15° is used. In addition, the outer shape of the
piezoelectric substrate 7, the first groove portions 22a, 22b, 24a, and
24b of the spindle portions 20a and 20b, and the second groove portions
17a (17b) and 18a (18b) of the vibrating arms 15a and 15b are formed
through etching processing using a photolithographic technology.

[0095]FIG. 1B is a cross-sectional view of FIG. 1A taken along line P-P
and is a diagram showing the arrangement of the excitation electrodes 30,
32, 34, and 36 formed in the vibrating arms 15a and 15b. The excitation
electrodes 30 and 34 are formed on the front and side faces of the groove
portions 17a (17b) and 18a (18b), and the excitation electrodes 32 and 36
are formed on both side faces of the vibrating arms 15a and 15b.

[0096] The excitation electrodes 30 and 36 and the excitation electrodes
32 and 34 are applied with voltages having opposite signs through the
above-described electrode pads. In other words, when positive voltages
are applied to the excitation electrodes 30 and 36, negative voltages are
applied to the excitation electrodes 32 and 34, and electric fields as
denoted by arrows shown in FIG. 1B are generated, whereby tuning fork
type resonator (flexural resonator) that is symmetrical to the center
line Cg passing through the center of gravity of the piezoelectric
resonator element 1 is excited.

[0097] In addition, by forming the groove portions 17a (17b) and 18a
(18b), the intensities of the electric fields are strong, whereby the
tuning fork type resonator can be excited more efficiently. In other
words, the CI (crystal impedance) of the piezoelectric resonator element
can be configured to be low.

[0098]FIG. 2 is a cross-sectional view of FIG. 1A taken along line Q-Q.
The spindle portions 20a and 20b, as shown in the plan view of FIG. 1A
and the cross-sectional view of FIG. 2, have a rectangular flat plate
shape, and the first groove portions 22a, 22b, 24a, and 24b are arranged
to be separated from each other in both end portions of each one of the
spindle portions 20a and 20b in the longitudinal direction of the
vibrating arms 15a and 15b, have line symmetry with respect to the
resonator center line C, and include a tip end-side first groove and a
base end-side first groove portion.

[0099] FIGS. 3A to 3C are plan views showing a modified example of the
first groove portions 22a, 22b, 24a, and 24b. As shown in FIG. 1A, since
the spindle portions 20a and 20b have the same shape, one spindle portion
20a will be described. The first groove portion 22a (22b) shown in FIG.
3A extends from the tip end edge of the spindle portion 20a in the
longitudinal direction of the vibrating arm 15a over the center portion
in the longitudinal direction and is formed to have line symmetry with
respect to the resonator center line C.

[0100] In the first groove portion 22a (22b) shown in FIG. 3B, the base
end portion of the first groove portion 22a (22b) is formed to be
continuous to the tip end portion of the second groove portion 17a (17b),
and the tip end portion of the first groove portion 22a (22b) extends up
to the tip end edge of the spindle portion 20a and is formed to have line
symmetry with respect to the resonator center line C.

[0101] The width of at least a part of the first groove portion 22a (22b)
shown in FIG. 3c is formed to be wider than the width of the second
groove portion 17a (17b).

[0102] In the piezoelectric resonator element 1, flexural resonator that
is symmetrical with respect to the center line Cg in the direction of the
vibrating arms 15a and 15b and torsional resonator that is symmetrical
with respect to the center line Cg, which pass the center of gravity, are
excited. By appropriately forming the excitation electrode, the resonator
mode to be principal resonator can be selected. FIG. 1A to 1C show an
example in which tuning fork resonator (flexural resonator) is configured
as a principal resonator mode.

[0103] As an example of a piezoelectric resonator element according to the
embodiment of the invention, a piezoelectric resonator element 1 is
formed by using a substrate acquired by cutting out a quartz crystal Z
substrate by rotating the electric axis (X axis) by θ (the range
from 0 degree to -15 degrees). In the vibrating arms 15a and 15b, the
second groove portions 17a, 17b, 18a, and 18b are formed, and, on the
front and rear faces of the spindle portions 20a and 20b disposed in the
tip end portions of the vibrating arms 15a and 15b, the first groove
portions 22a, 22b, 24a, and 24b are formed.

[0104] In other words, by appropriately selecting the cutting angle
θ, the first groove portions 22a, 22b, 24a, and 24b, and the second
groove portions 17a, 17b, 18a, and 18b, two resonator modes are combined
by approaching the resonance frequencies fF and fT of the
flexural resonator (tuning fork resonator) and the torsional resonator
excited in the piezoelectric resonator element 1, whereby a tuning
fork-type resonator element is configured of which the
frequency-temperature characteristics of the flexural resonator of the
principal resonator are improved and the size is decreased.

[0105] Now, units that allow the resonance frequencies fF and fT
of the flexural resonator and the torsional resonator of the
piezoelectric resonator element according to the embodiment of the
invention to approach each other will be described with reference to
FIGS. 4A to 4C.

[0106] FIGS. 4A to 4C are diagrams qualitatively illustrating the changes
in the resonance frequency fF of the flexural resonator and the
resonance frequency fT of the torsional resonator, which are excited
in the piezoelectric resonator element (tuning fork-type piezoelectric
resonator element), according to the first groove portions 22a (22b) and
24a (24b) of the spindle portions 20a and 20b, the second groove portions
17a and 17b of the vibrating arms 15a and 15b, and the thickness h of the
vibrating arms 15a and 15b. In addition, A and B denoted in the
horizontal axis in FIGS. 4A and 4B represent the shapes of the beam
(vibrating arm) 15, A represents a case before a groove is formed in the
beam 15, and B represents a case where a groove is formed. FIG. 4C is a
case where the plate thickness of the beam 15 is changed.

[0107] Here, the resonance frequencies of the flexural resonator and the
torsional resonator exited in the beam 15 before formation of a groove
portion are denoted by fF and fT, and the resonance frequencies
in a case where a groove portion 22a (22b) is formed in the tip end
portion 15 of the beam 15 are denoted by f'F and f'T. As shown
in FIG. 4A, in a case where the groove portion 22a (22b) is formed in the
tip end portion of the beam (vibrating arm) 15, while both the resonance
frequencies f'F and f'T of the flexural resonator and the
torsional resonator rise, the degree dfF=(f'F-fF) of
increase in the frequency of the flexure resonator is higher than the
degree dfT=(f'T-fT) of increase in the frequency of the
torsional resonator.

[0108] On the other hand, as shown in FIG. 4B, in a case where the groove
portion 17a (17b) is formed in the center portion of the beam (vibrating
arm) 15, while the resonance frequencies f'T and f'F of the
torsional resonator and the flexural resonator fall, the degree
dfT=(fT-f'T) of decrease in the frequency of the torsional
resonator is higher than the degree dfF=(fF-f'F) of
decrease in the frequency of the flexural resonator.

[0109] In addition, as shown in FIG. 4C, in a case where the plate
thickness h of the beam 15 is increased, while the frequency f'F of
the flexural resonator is slightly lower than the original frequency
fF, the resonance frequency f'T of the torsional resonator is
higher than the original frequency fT.

[0110] As above, by appropriately selecting the position of the groove
portion formed in the beam (vibrating arm) 15 and the thickness of the
beam (vibrating arm) 15, the resonance frequencies of the flexural
resonator and the torsional resonator can be allowed to approach each
other.

[0111] FIGS. 5A to 5C are plan views of the spindle portions 20a and 20b
in a case where only a concave portion and a groove portion formed on the
front and rear faces of the spindle portions 20a and 20b are changed
without changing the outer shape of the piezoelectric resonator element
1. FIGS. 5A and 5B are examples in which concave portions 21a (21b) and
21'a (21'b) facing each other so as to have line symmetry with respect to
the resonator center line C are formed in the center portions of the
front and rear faces of the spindle portions 20a and 20b along the
longitudinal direction of the vibrating arms 15a and 15b. The areas of
the concave portion 21a (21b) and 21'a (21'b) shown in FIG. 5B are formed
to be larger than the areas of the concave portions 21a (21b) and 21'a
(21'b) shown in FIG. 5A. FIG. 5C is an example in which groove portions
22a (22b) and 24a (24b) are formed so as to have line symmetry with
respect to the resonator center line C along the longitudinal direction
of the vibrating arms 15a and 15b from the tip end over the center
portion on the front and rear faces of the spindle portions 20a and 20b.

[0112]FIG. 6 is a diagram showing the resonance frequencies fF and
fF of the flexural resonator and the torsional resonator of the
piezoelectric resonator element 1 including the spindle portions 20a and
20 having the shapes shown in FIGS. 5A to 5C and a difference frequency
Δf=(fT-fF) that are acquired through simulations using a
finite element method. In the figure, the left side of the vertical axis
represents the resonance frequencies fF and fT, and the right
side of the vertical axis represents the difference frequency Δf.
In addition, the horizontal axis represents reference signs a, b, and c
in correspondence with the piezoelectric resonator element 1 including
the spindle portions 20a and 20 having the shapes shown in FIGS. 5A to
5C.

[0113] When the resonance frequencies of a and b shown in FIG. 6 are
compared with each other, it is understood that, as the area of the
concave portions is increased, the difference frequency Δf
decreases in a case where the sizes of the concave portions of the
spindle portions 20a and 20b are changed without changing the outer shape
of the piezoelectric resonator element 1. As shown in FIG. 4A, this can
be described also based on that, as the mass of the tip end portion of
the beam (vibrating arm) 15 is decreased, the increase in the frequency
of the flexural resonator is larger than the increase in the frequency of
the torsional resonator, and the difference frequency
Δf=(fT-fF) decreases. In addition, it can be described
based on FIG. 4A that the frequency of the flexural resonator of b is
higher than the frequency of the flexural resonator of a.

[0114] In addition, c shown in FIG. 6 is an example in which groove
portions 22a (22b) and 24a (24b) are formed in the tip end portions of
the spindle portions 20a and 20b, and it is presented that the difference
frequency Δf=(fT-fF) can be described further. By
configuring the difference frequency Δf=(fT-fF) to be
small, for example, by configuring the value of
Δf/((fT-fF)/2) to be 10% or less, the combination of the
flexure resonator and the distortion resonator is dense, and the
frequency-temperature characteristics of the flexure resonator as the
principal resonator are improved.

[0115] FIGS. 7A to 7C qualitatively illustrate the appearance of improving
the frequency-temperature characteristics of flexural resonator of
principal resonator by combining the flexural resonator and torsional
resonator excited in the piezoelectric resonator element 1, by using
diagrams. Generally, the frequency-temperature characteristics Δf/f
(=(f-f0)/f, here, f0 is a frequency at predetermined
temperature) can be represented in a polynomial of temperature T as shown
in Equation (1).

Δf/f=α(T-T0)+β(T-T0)2+γ(T-T0)-
3+ . . . (1)

[0116]FIG. 7A shows a quadratic curve with respect to temperature T as
the frequency-temperature characteristics of the flexural resonator that
is the principal resonator. FIG. 7B shows the frequency-temperature
characteristics of the torsional resonator, and a frequency Δf/f is
approximated to a first-order equation with respect to temperature T.
FIG. 7C is a diagram showing the frequency-temperature characteristics of
the flexural resonator as the principal resonator in a case where the
flexure resonator and the torsional resonator are combined. By combining
the torsional resonator with the flexural resonator as the principal
resonator, the first-order coefficient α and the second-order
coefficient β of the polynomial Δf/f representing the
frequency-temperature characteristics of the flexural resonator can be
configured to be almost zero, and the frequency-temperature
characteristics of the flexural resonator of the principal resonator can
be approximated by a third-order coefficient γ so as to represent a
cubic curve (third-order characteristics) in a desired temperature range
including room temperature as shown in FIG. 7C.

[0117]FIG. 8 is a diagram representing the degree of combination of the
flexural resonator and the torsional resonator acquired through a
simulation in a case where the plate thickness h of the vibrating arms
15a and 15b of the piezoelectric resonator element 1 (tuning fork type
quartz crystal resonator element) is changed. The resonance frequency
fF of the flexural resonator is approximately flat with respect to
the thickness h and slightly decreases in accordance with an increase in
the thickness h.

[0118] On the other hand, the resonance frequency fT of the torsional
resonator increases in approximately proportional to an increase in the
thickness h. In the example shown in FIG. 8, it can be understood that
the combination increases at a plate thickness h slightly smaller than 86
μm.

[0119]FIG. 9A is a diagram illustrating the first-order coefficient
α and the second-order coefficient β of the flexural resonator
and the first-order coefficient α' and the second-order coefficient
β' of the torsional resonator, which are acquired through a
simulation, excited in the piezoelectric resonator element 1. In the
figure, the first-order coefficient α and the second-order
coefficient β are denoted by a diamond .diamond-solid. and a square
.box-solid., and the first-order coefficient α' and the
second-order coefficient β' of the torsional resonator are denoted
by a white diamond ⋄ and a white square quadrature. From FIG.
9A, it can be understood that the first-order coefficient α' of the
torsional resonator is larger than the other coefficients. In other
words, in the torsional resonator, the first-order coefficient α'
is dominant.

[0120] In addition, it can be understood that the first-order coefficient
α and the second-order coefficient β of the flexural resonator
are extremely small in the range of 84 μm to 85 μm as the plate
thickness h of the vibrating arms 15a and 15b in the example of FIGS. 9A
and 9B.

[0121]FIG. 9B is a diagram illustrating the first-order coefficients and
the second-order coefficients α, β, α' and, β' of
the flexural resonator and the torsional resonator with respect to the
plate thickness h in a case where the plate thickness h of the vibrating
arms 15a and 15b is changed in the range of 82 μm to 86 μm. In the
example of FIG. 9B, it is determined that both the first-order
coefficient α and the second-order coefficient β of the
flexural resonator are approximately zero near the plate thickness h=84.5
μm. In addition, it can be understood that the second-order
coefficient β' of the torsional resonator is approximately zero near
the plate thickness h=84.5 μm.

[0122] In other words, in the example of the piezoelectric resonator
element 1 shown in FIGS. 9A and 9B, by setting the plate thickness h to
84.5 μm, both the first-order coefficient α and the second-order
coefficient β of the frequency-temperature characteristics of the
flexural resonator as the principal resonator can be zero. Accordingly,
the frequency-temperature characteristics of the flexural resonator
represent a cubic curve, and the frequency-temperature characteristics
are markedly improved. In addition, by arranging the spindle portions 20a
and 20b, the vibrating arms are shortened, whereby a small-size
piezoelectric resonator element 1 can be acquired.

[0123] In addition, by emitting laser beams to the electrodes formed on
the front and rear faces of the spindle portions 20a and 20b, the
electrodes formed inside the first groove portions 22a, 22b, 24a, and
24b, and the electrodes formed in the vibrating arms 15a and 15b, the
degree of combination of the flexural resonator and the torsional
resonator excited in the tuning fork type piezoelectric resonator can be
delicately adjusted.

[0124] Furthermore, when frequency variations due to a falling impact and
the like are considered, there is a case where the electrodes for the
spindle portions are preferably formed only inside the first groove
portions by avoiding the electrodes (particularly, the tip end portions)
formed on the front and rear faces of the spindle portion.

[0125] As shown in FIGS. 1A and 1B, according to the piezoelectric
resonator element (tuning fork type resonator element) 1 according to the
embodiment of the invention, the spindle portions are formed in the tip
end portions of the vibrating arms, the first groove portions extending
in a linear shape along the longitudinal direction of the resonator arms
are formed on the front and rear faces of the spindle portions, and the
second groove portions are formed on the front and rear faces along the
resonator center line of the vibrating arms. By configuring as such, the
flexural resonator and the torsional resonator excited in the tuning fork
type piezoelectric resonator element 1 are allowed to approach each other
and can be combined together. Accordingly, the frequency-temperature
characteristics of the flexural resonator as the principal resonator of
the flexure-torsional combined resonator have third-order
characteristics, whereby there is an advantage that a miniaturized
piezoelectric resonator element having superior temperature
characteristics can be acquired.

[0126] In addition, as shown in FIG. 1A, the base portion of the
piezoelectric resonator element (tuning fork type piezoelectric resonator
element) 1 includes the base portion main body, the connection portions,
and the support arms having an "L" shape and a reverse "L" shape, the end
portions of the "L" shape and the reverse "L" shape are connected to each
other, and each connection portion is configured to be connected to the
center of one end portion of the base portion main body through the
connection portion. Accordingly, the resonator energy leaking to the
support arms from the vibrating arms can be reduced, whereby the CI value
is small, and the impact resistance is improved. As a result, there is an
advantage of acquiring a piezoelectric resonator element having no
problem of frequency variations due to a damage, a destruction, or the
like that is caused by an impact.

[0127] The piezoelectric resonator element (tuning fork type piezoelectric
resonator element) 1 is configured in which the cutting angle of the
piezoelectric substrate 7 shown in FIG. 1A is rotated around the electric
axis (X axis) in the range of 0 degree to -15 degrees. By selecting the
cutting angle as such, the first-order coefficient and the second-order
coefficient of the polynomial representing the frequency-temperature
characteristics of the flexure-torsional combined resonator can be
configured to be approximately zero, and there is an advantage of
acquiring a piezoelectric resonator element having superior temperature
characteristics.

[0128] In addition, by configuring the piezoelectric resonator element 1
in which the first groove portions 22a to 24b are formed as shown in FIG.
1A, the frequency-temperature characteristics of the flexure resonator of
the flexure-torsional combined resonator have third-order characteristics
with respect to the temperature, and there are an advantage of acquiring
the piezoelectric resonator element having superior temperature
characteristics and an advantage of forming the lead electrodes that
electrically connect the excitation electrodes on the flat faces of the
spindle portions 20a and 20b.

[0129] In addition, by configuring the piezoelectric resonator element in
which the first groove portions 22a to 24b are formed as shown in FIGS.
3A to 3C, the frequency-temperature characteristics of the principal
resonator of flexure-torsional combined resonator represent third-order
characteristics with respect to the temperature, and there is an
advantage of improving the temperature characteristics. Furthermore,
there is an advantage of forming the lead electrodes electrically
connecting the excitation electrodes on the flat faces of the spindle
portion 20a in the example shown in FIG. 3A, there is an advantage of
easily forming masks used for forming the first and second groove
portions in the example shown in FIG. 3B, and there is an advantage of
easily combining the flexure resonator frequency and the torsional
resonator frequency in the example shown in FIG. 3c by appropriately
setting the width of the first groove portion.

[0130]FIG. 10 is a cross-sectional view showing the configuration of a
piezoelectric resonator 2 according to a second embodiment of the
invention. The piezoelectric resonator 2 includes the above-described
piezoelectric resonator element 1 and a package that houses the
piezoelectric resonator element 1. The package is configured by a package
main body 40 formed in a rectangular box shape and a lid member 52 having
a window member 54 formed from glass or the like.

[0131] The package main body 40, as shown in FIG. 10, is formed by
laminating a first substrate 41 as an insulating substrate, a second
substrate 42, and a third substrate 43, and is formed by molding a
ceramic green sheet made of aluminum oxide so as to be in the shape of a
box as an insulating material and sintering the molded ceramic green
sheet. In addition, a plurality of mounting terminals 45 is formed on the
bottom face of the first substrate 41 that is located on the outer side.

[0132] In the third substrate 43, the center portion is removed, and, on
the upper peripheral edges of the third substrate 43, metal seal rings
44, for example, made from Kovar or the like are formed.

[0133] A concave portion housing the piezoelectric resonator element 1 is
formed by the third substrate 43 and the second substrate 42. At
predetermined positions located on the upper face of the second substrate
42, a plurality of element mounting pads 47 that are electrically
connected to the mounting terminals 45 by conductive bodies 46 is
disposed.

[0134] The positions of the element mounting pads 47 are arranged so as to
be in correspondence with pad electrodes (not shown in the figure) formed
in support arms 12b and 12c when the piezoelectric resonator element 1 is
placed.

[0135] In the configuration of the piezoelectric resonator 2, the element
mounting pad 47 of the package main body 40 is coated with a conductive
bonding agent 50, for example, any one of an epoxy-based bonding agent, a
polyimide-based bonding agent, and a bismaleimide-based bonding agent,
and the piezoelectric resonator element 1 is placed thereon so as to
apply a weight.

[0136] Then, in order to harden the conductive bonding agent 50 of the
piezoelectric resonator element 1 mounted in the package main body 40,
the package main body is placed in a predetermined high-temperature
furnace for a predetermined time. After an annealing process is
performed, a part of a frequency adjusting metal film formed in spindle
portions 20a and 20b and the vibrating arms 15a and 15b is transpired by
emitting laser beams from the upper side, whereby coarse frequency
adjustment is performed. Then, the lid member 52 including the glass
window portion 54 is seam-welded to the seal ring 44 formed on the upper
face of the package main body 40.

[0137] Before sealing a through hole 48 of the package, a heating process
is performed. Then, the package is vertically reversed, and a filler 48a
of a metal sphere is placed on a level difference portion located inside
the through hole 48. As the filler 48a, a gold-germanium alloy or the
like may be used. The filler 48a is melted by emitting laser beams
thereto, whereby the through hole 48 is sealed, and the inside of the
package is formed to be vacuum. In addition, laser beams are emitted to
the inside of the package from the outside of the package through the
window member 54, and the frequency adjusting metal film formed in the
vibrating arms 15a and 15b is transpired so as to perform delicate
frequency adjustment, whereby the piezoelectric resonator 2 is completed.

[0138] The transformation of the piezoelectric resonator element 1 that
occurs when an impact such as falling is applied to the piezoelectric
resonator 2 having the configuration shown in FIG. 10 will be described.
When an impact is applied in a direction perpendicular to the principal
face of the package of the piezoelectric resonator 2, in the
piezoelectric resonator element 1, arm support portions 12b and 12c that
can be easily transformed with the element mounting pad 47 used as a
point of support are transformed toward the bottom face of the package
main body 40. Next, this transformation is reflected to an outer end
frame 12e of a base portion 10, and the transformation propagates to the
center portion of the base portion main body 12a, whereby the entirety
including the base portion main body 12a is sunk to the bottom face side
of the package main body 40. As a result, the tip end sides of the
vibrating arms 15a and 15b are transformed toward the package bottom
face. In other words, in the structure of the base portion 10, by
connecting the base portion main body 12a to the support arms 12b and 12c
through the connection portions 12d, an impact applied thereto is
configured to be alleviated by the structure of the base portion 10.

[0139] As shown in the cross-sectional view of FIG. 10, the piezoelectric
resonator 2 is configured by allowing the flexural resonator and
torsional resonator excited in the tuning fork type piezoelectric
resonator element to approach each other and housing the tuning fork type
piezoelectric resonator element 1 in which the flexure-torsional combined
resonator is excited in an insulating substrate 40, whereby there is an
advantage of acquiring a piezoelectric resonator that has a high Q value
due to its small size and has superior frequency-temperature
characteristics.

[0140]FIG. 11 is a cross-sectional view showing the configuration of a
piezoelectric oscillator 3 according to a third embodiment of the
invention. The piezoelectric oscillator 3 includes: the above-described
piezoelectric resonator element 1; an IC component 78 that excites the
piezoelectric resonator element 1; a package main body 60 that seals the
piezoelectric resonator element 1 so as to form a vacuum state and houses
the IC component 78; and a lid member 75 that includes a window member
75a. The coarse adjustment through emitting laser beams to the
piezoelectric resonator element 1, a technique for delicate adjustment,
or a technique of sealing the through hole 68 by forming the inside of
the package to be in a vacuum state, and the like are similar to those of
the piezoelectric resonator 2, and are not described here. The IC
component 78 is electrically conducted and connected to the IC component
mounting pad 69 of the package main body 60 using a metal bump 76 or the
like.

[0141] In the piezoelectric oscillator 3 shown in FIG. 11, although an
example is shown in which the IC component 78 is not sealed in an
air-tight manner, it may be configured such that the IC component 78 is
arranged inside the package and is sealed in an air-tight manner.

[0142] As shown in the cross-sectional view of FIG. 11, the piezoelectric
oscillator is configured so as to include: the tuning fork type
piezoelectric resonator element 1 in which the flexural resonator and the
torsional resonator approach each other, and the flexure-torsional
combined resonator is excited; an IC component 78; and a package 60 that
houses the tuning fork type piezoelectric resonator element and the IC
component, whereby there is an advantage of acquiring a small-size
piezoelectric oscillator having superior frequency-temperature
characteristics.

[0143] FIGS. 12A to 12C are diagrams showing the configuration of a
resonator gyro sensor 4 according to a fourth embodiment of the invention
and, in the figures, the lid body is not illustrated. FIG. 12A is a plan
view of the resonator gyro sensor 4, and FIG. 12B is a cross-sectional
view taken along line P-P.

[0144] The resonator gyro sensor 4 includes a resonator gyro element 80
and a package that houses the resonator gyro element 80. The package
includes an insulating substrate (package main body) 79 and a lid body
that seals the insulating substrate 79 in an air-tight manner.

[0145] The resonator gyro element 80 includes a base portion that includes
a base portion main body 81 and one pair of detecting vibrating arms 85a
and 85b that protrude from two end edges of the base portion main body
81, which face each other, on the same line. In addition, the resonator
gyro element 80 includes one pair of first connecting arms 82a and 82b
protruding from the other two end edges of the base portion main body 81,
which face each other, on the same line in a direction perpendicular to
the detecting vibrating arms 85a and 85b and one pair of driving
vibrating arms 83a and 83b and one pair of driving vibrating arms 84a and
84b that protrude from the tip end portions of the first connecting arms
82a and 82b in both directions perpendicular thereto.

[0146] In addition, the base portion includes one pair of second
connecting arms that protrude from the other two end edges of the base
portion main body 81, which face each other, on the same line in a
direction perpendicular to the detecting vibrating arms 85a and 85b and
one pair of support arms 86a and 86b and one pair of support arms 87a and
87b that protrude from the tip end portions of the second connecting arms
in both directions perpendicular thereto and are arranged between the
detecting vibrating arms 85a and 85b and the driving vibrating arms 83a
and 83b and 84a and 84b.

[0147] Furthermore, excitation electrodes are formed at least one pair of
the detecting vibrating arms 85a and 85b and one pair of the driving
vibrating arms 83a and 83b and 84a and 84b. In the support arms 86a and
86b and 87a and 87b, a plurality of electrode pads (not shown in the
figure) is formed, and the electrode pads and the excitation electrodes
are electrically connected to each other.

[0148]FIG. 12C is a schematic plan view showing the operation of the
resonator gyro element. The resonator gyro sensor 4, in a state in which
an angular velocity is not applied thereto, the driving vibrating arms
83a, 83b, 84a, and 84b perform flexural resonator in a direction denoted
by arrow E. At this time, since the driving vibrating arms 83a and 83b
and the driving vibrating arms 84a and 84b are vibrated so as to have
line symmetry with respect to a line that passes through the center G of
gravity and extends in the Y' axis direction, the base portion main body
81, the connecting arms 82a and 82b, and the detecting vibrating arms 85a
and 85b hardly vibrate.

[0149] When an angular velocity ω for Z' axis rotation is applied to
the resonator gyro sensor 4, a Coriolis force works on the driving
vibrating arms 83a, 83b, 84a, and 84b, and the first connecting arms 82a
and 82b, whereby new resonator is excited. This resonator is resonator in
the circumferential direction with respect to the center G of gravity. At
the same time, detection resonator is excited in the detecting vibrating
arms 85a and 85b in accordance with the resonator. By detecting
distortion occurring in accordance with the resonator using the detecting
electrodes formed in the detecting vibrating arms 85a and 85b, the
angular velocity is acquired.

[0150] According to the features of the resonator gyro sensor 4 of the
embodiment of the invention, the spindle portions 26 are disposed in the
tip end portions of the driving vibrating arms 83a, 83b, 84a, and 84b,
and first groove portions 27 are formed on the front and rear face of
each spindle portion 26 along the longitudinal direction of the vibrating
arms so as to have line symmetry with respect to the resonator center
line. In addition, in the driving vibrating arms 83a, 83b, 84a, and 84b,
second groove portions 28 are formed along the longitudinal direction of
the vibrating arms so as to have line symmetry with respect to the
resonator center line. By appropriately selecting the cutting angle
θ of the piezoelectric resonator substrate of the resonator gyro
element 80 and the first groove portion 27 of the spindle portion 26, the
second groove portions 28 of the driving arms 83a, 83b, 84a, and 84b, and
the plate thickness of the driving arms 83a, 83b, 84a, and 84b, the
resonance frequencies fF and fT of the flexural resonator and
the torsional resonator excited in the resonator gyro element 80 can
approach each other. The frequency-temperature characteristics of the
flexural resonator of the principal resonator are improved by combining
two resonator modes, and the driving vibrating arms and the detecting
vibrating arms are shortened by arranging the spindle portions 26,
whereby the small-size resonator gyro sensor 4 can be configured.

[0151] As shown in FIG. 12A, the resonator gyro element 80 is configured
in which the spindle portions 26 are formed in the tip end portions of
the driving vibrating arms 83a to 84b, the first groove portions 27
extending in a linear shape along the longitudinal direction of the
vibrating arms on the front and rear faces of the spindle portions 26,
and the second groove portions 28 are formed on the front and rear faces
of the driving vibrating arms along the resonator center line. By
configuring such a resonator gyro element 80, the frequency-temperature
characteristics of the flexural resonator that is the principal resonator
of the flexure-torsional combined resonator excited in each driving
vibrating arm represent third-order characteristics with respect to the
temperature, and accordingly, there is an advantage of acquiring the
resonator gyro element that has superior temperature characteristics and
a small size.

[0152] In addition, as shown in FIG. 12A, by configuring a resonator gyro
sensor by housing the resonator gyro element in a package, the
frequency-temperature characteristics of the principal resonator of the
flexure-torsional combined resonator excited in each driving vibrating
arm is improved, and there is an advantage of acquiring a small-size
resonator gyro sensor by arranging the spindle portions.

[0153]FIG. 13 is a schematic configuration diagram showing the
configuration of an electronic apparatus according to the embodiment of
the invention. In the electronic apparatus 5, the piezoelectric resonator
2 described in the above-described second embodiment is included. As
examples of the electronic apparatus 5 using the piezoelectric resonator
2, there are mobile electronic apparatuses such as a cellular phone, a
digital camera, and a video camera. In such electronic apparatuses 5, the
piezoelectric resonator 5 is used as a reference signal source, and, by
including the small-size piezoelectric resonator 2 having high precision,
an electronic apparatus that has superior mobility due to its small size
and has superior characteristics can be provided.

[0154] As shown in FIG. 13, by configuring the electronic apparatus that
includes the piezoelectric resonator 2 shown in FIG. 10, there is an
advantage of improving the stability of the frequency source of the
electronic apparatus. In addition, by configuring the electronic
apparatus including the resonator gyro sensor shown in FIG. 12A, there is
an advantage of reducing the change in the sensitivity of the angular
velocity according to the temperature.

[0155] In addition, regarding the groove portion, the first groove
portions 22a and 22b and the first groove portions 24a an 24b shown in
FIGS. 1A and 1B may be connected so as to form a so-called slit shape
(through shape). Such a configuration may be applied to the embodiments
shown in FIGS. 10 to 13.

[0156] FIGS. 14A and 14B show another embodiment of the invention.

[0157] In the exemplary embodiment shown in FIG. 14A, the spindle portions
20a and 20b form a concave shape in the center portions of the tip end
edges by forming notch portions (through portions) 22ab and 24ab as
groove portions that are symmetrical with respect to the resonator center
C in which the first groove portions 22a located on the front and rear
sides are connected, and mass portions 21 are formed on both sides of
each notch portion. In other words, in this embodiment, the mass portions
21 are arranged on both sides along the resonator center C with being
separated from the resonator center C.

[0158] In the example in which the notch portions symmetrical with respect
to the resonator center C are formed in the center portions of the tip
end edges, since a shape is formed for which it is difficult for the
effect of a difference in the etching speed according to the direction of
the crystal axis, which is caused by the anisotropy unique to the
piezoelectric substrate, to appear more than in the case of a bottomed
groove portion, the mass portions 21 are arranged on both sides along the
resonator center C with being separated from the resonator center C.

[0159] The cross-sectional view shown in FIG. 14B is a diagram showing the
arrangement of excitation electrodes 30, 32, 34, and 36 formed in the
vibrating arms 15a and 15b. The excitation electrodes 30 and 34 are
formed on the front faces and the side faces of the groove portions 17a
(17b) and 18a (18b), and the excitation electrodes 32 and 36 are formed
on both side faces of the vibrating arms 15a and 15b.

[0160] The excitation electrodes 30 and 36 and the excitation electrodes
32 and 34 are applied with voltages having opposite signs through the
above-described electrode pads. In other words, when positive voltages
are applied to the excitation electrodes 30 and 36, negative voltages are
applied to the excitation electrodes 32 and 34, and electric fields as
denoted by arrows shown in FIG. 14B are generated, whereby tuning fork
type resonator (flexural resonator) that is symmetrical to the center
line Cg (hereinafter, referred to as a center line of center of gravity)
passing through the center of gravity of the piezoelectric resonator
element 1 is excited.

[0161] In addition, by forming the groove portions 17a (17b) and 18a
(18b), the intensities of the electric fields are strong, whereby the
tuning fork type resonator can be excited more efficiently. In other
words, the CI (crystal impedance) of the piezoelectric resonator element
can be configured to be low.

[0162]FIG. 15 is a plan view showing another exemplary embodiment (only
one spindle portion 20a is shown) of the spindle portion 20a (20b).
Through holes 23a (23b) that are symmetrical with respect to the
resonator center C are formed within the plane of the spindle portion 20a
(20b) closer to the vibrating arm 15a (15b) than a notch portion 22ab
(24ab) shown in FIG. 15A. The mass portions 21 are arranged along the
resonator center C on both sides with being separated from the resonator
center C. By separating the notch portion 22ab (24ab) and a through hole
23a (23b) from each other, abridging portion 29a (29b) that connect the
mass portions 21 having the resonator center C interposed therebetween is
formed.

[0163] In addition, the width of the through hole 23a (23b) may be equal
to or different from the width of the notch portion 22ab (24ab).

[0164] In the spindle portion 20a (20b) shown in FIG. 14A, there is a
concern that the mass portions 21 located on the left and right sides of
the resonator center C may unnecessarily vibrate when the piezoelectric
resonator element 1 is excited, and the vibrating arms 15a and 15b
vibrate in the flexure mode. In contrast to this, by arranging the
bridging portion 29a (29b) as in the embodiment shown in FIG. 15, the
unnecessary resonator of the mass portion 21 is suppressed, and the
piezoelectric resonator element 1 that is strong for an impact and the
like is acquired.

[0165]FIG. 16 is a plan view showing yet another exemplary embodiment
(only one spindle portion 20a is shown in the figure) of the spindle
portion 20a (20b). As shown in the plan view of FIG. 16, a spindle
portion 20a (20b) has a through hole 23a (23b) that is symmetrical with
respect to the resonator center C in the center portion of the area of
the spindle portion 20a (20b). As above, by arranging the through hole
23a (23b) in the center portion of the area of the spindle portion 20a
(20b), the mass portions 21 are arranged along the resonator center C on
both sides with being separated from the resonator center C.

[0166]FIG. 17 is a plan view showing still another exemplary embodiment
(only one spindle portion 20a is shown in the figure) of the spindle
portion 20a (20b). Each spindle portion 20a (20b) includes a through hole
23a (23b) that is symmetrical with respect to the resonator center C in
the side end of the base portion, and the through hole 23a (23b) is
connected (communicated with) to groove portions 17a and 17b(18a and 18b)
of each vibrating arm 15a (15b). The mass portions 21 are arranged along
the resonator center C on both sides with being separated from the
resonator center C.

[0167] In the piezoelectric resonator element 1, flexural resonator that
is symmetrical with respect to the center line Cg of the center of
gravity in the direction of the vibrating arms 15a and 15b and torsional
resonator that is symmetrical with respect to the center line Cg of the
center of gravity, which pass the center of gravity, are excited. By
appropriately forming the excitation electrode, the resonator mode to be
principal resonator can be selected. The exemplary embodiment shown in
FIGS. 14A and 14B is an example in which tuning fork resonator (flexural
resonator) is configured as a principal resonator mode.

[0168] As an example of a piezoelectric resonator element according to the
embodiment of the invention, a piezoelectric resonator element 1 is
formed by using a substrate acquired by cutting out a quartz crystal Z
substrate by rotating the electric axis (X axis) by θ (the range
from 0 degree to -15 degrees). In the vibrating arms 15a and 15b, groove
portions 17a (17b) and 18a (18b) are formed, and, in the spindle portions
20a and 20b, mass portions are formed along the resonator center C on
both sides with being separated from the resonator center C.

[0169] In other words, by appropriately setting the cutting angle θ,
the thickness of the piezoelectric substrate 8, the notch portions 22a
and 22b of the spindle portions 20a and 20b or the through holes 23a and
23b and the groove portions 17a, 17b, 18a, and 18b, two resonator modes
are combined by approaching the resonance frequencies fF and fT
of the flexural resonator (tuning fork resonator) and the torsional
resonator excited in the piezoelectric resonator element 1, whereby a
tuning fork-type resonator element is configured of which the
frequency-temperature characteristics of the flexural resonator as the
principal resonator are improved and the size is decreased.

[0170] Here, units that allow the resonance frequencies fF and
fT of the flexural resonator and the torsional resonator to approach
each other are similar to those described with reference to FIGS. 4A to
4C.

[0171] FIGS. 4A to 4C can be used as diagrams qualitatively illustrating
the changes in the resonance frequency fF of the flexural resonator
and the resonance frequency fT of the torsional resonator, which are
excited in the piezoelectric resonator element (tuning fork-type
piezoelectric resonator element) 1 shown in FIG. 14A, according to the
notch portions 22a and 22b of the spindle portions 20a and 20b, the
groove portions 17a, 17b, 18a, and 18b of the vibrating arms 15a and 15b,
and the thickness h of the vibrating arms 15a and 15b.

[0172] In addition, A and B denoted in the horizontal axis in FIGS. 4A and
4B represent the shapes of the beam (vibrating arm) 15, A represents a
case before a notch portion is formed in the beam 15, and B represents a
case where a notch portion is formed. In FIG. 4C, a case where the plate
thickness h of the beam 15 is formed to be thicker than A is represented
as B.

[0173] In this embodiment, by combining the flexural resonator and
torsional resonator excited in the piezoelectric resonator element 1, the
appearance of improving the frequency-temperature characteristics of
flexural resonator of principal resonator is similar to that described
with reference to FIGS. 7A to 7C.

[0174]FIG. 7A shows a quadratic curve with respect to temperature T as
the frequency-temperature characteristics of the flexural resonator that
is the principal resonator. FIG. 7B shows the frequency-temperature
characteristics of the torsional resonator, and a frequency Δf/f is
approximated to a first-order equation with respect to temperature T.
FIG. 7C is a diagram showing the frequency-temperature characteristics of
the flexural resonator as the principal resonator in a case where the
flexure resonator and the torsional resonator are combined. By combining
the torsional resonator with the flexural resonator as the principal
resonator, the first-order coefficient α and the second-order
coefficient β of the polynomial Δf/f representing the
frequency-temperature characteristics of the flexural resonator can be
configured to be almost zero, and the frequency-temperature
characteristics of the flexural resonator of the principal resonator can
be approximated by a third-order coefficient γ so as to represent a
cubic curve as shown in FIG. 7C.

[0175] In addition, in a case where the plate thickness h of the vibrating
arms 15a and 15b of the piezoelectric resonator element 1 is changed, the
degree of combination between the flexural resonator and the torsional
resonator acquired as a simulation result is the same as that shown in
FIG. 8. In other words, the resonance frequency fF of the flexural
resonator is approximately flat with respect to the thickness h and
slightly decreases in accordance with an increase in the thickness h.

[0176] On the other hand, the resonance frequency fT of the torsional
resonator increases in approximately proportional to an increase in the
thickness h. In the example shown in FIG. 8, it can be understood that
the combination increases at a plate thickness h slightly smaller than 86
μm.

[0177] Also in this embodiment, a simulation result of the first-order
coefficient α and the second-order coefficient β of the
flexural resonator and the first-order coefficient α' and the
second-order coefficient β' of the torsional resonator excited in
the piezoelectric resonator element 1 in which the groove portion
(through portion) is formed along the resonator center C of the spindle
portion 20a (20b) is the same as the trend of that shown in FIG. 9B. In
the figure, the first-order coefficient α and the second-order
coefficient β are denoted by a diamond .diamond-solid. and a square
.box-solid. respectively, and the second-order coefficient β' of the
torsional resonator is denoted by a white square quadrature. Since the
first-order coefficient α' of the torsional resonator has a very
large value so as to be out of the range of the graph, it is not shown in
the figure. In other words, in the torsional resonator, the first-order
coefficient α' is dominant.

[0178]FIG. 9B is a diagram, as described above, illustrating the
first-order coefficients and the second-order coefficients α,
β, α' and, β' of the flexural resonator and the torsional
resonator with respect to the plate thickness h in a case where the plate
thickness h of the vibrating arms 15a and 15b is changed in the range of
82 μm to 86 μm. In the example of FIG. 9B, it is determined that
both the first-order coefficient α and the second-order coefficient
β of the flexural resonator are approximately zero near the plate
thickness h=84.5 μm. In addition, it can be understood that the
second-order coefficient β' of the torsional resonator is
approximately zero near the plate thickness h=84.5 μm.

[0179] In other words, in the example of the piezoelectric resonator
element 1 shown in FIG. 9B, by setting the plate thickness h to 84.5
μm, both the first-order coefficient α and the second-order
coefficient β of the frequency-temperature characteristics of the
flexural resonator as the principal resonator can be zero. Accordingly,
the frequency-temperature characteristics of the flexural resonator
represent a cubic curve, and the frequency-temperature characteristics
are markedly improved. In addition, by arranging the spindle portions 20a
and 20b, the vibrating arms are shortened, whereby a small-size
piezoelectric resonator element 1 can be acquired.

[0180] In addition, by emitting laser beams to the electrodes formed on
the front and rear faces of the spindle portions 20a and 20b, the
electrodes of the groove portions 17a, 17b, 18a, and 18b, the electrodes
formed in the vibrating arms 15a and 15b, and the like, the degree of
combination of the flexural resonator and the torsional resonator excited
in the tuning fork type piezoelectric resonator can be delicately
adjusted.

[0181] FIGS. 18A to 18F are diagrams showing the shapes in which a through
portion-type groove portion is formed in the spindle portion 20a of the
piezoelectric resonator element 1. FIG. 18A is a plan view of a
rectangle-shaped spindle portion 20a that has not been processed at all,
FIG. 18B is a plan view of a spindle portion 20a in which a notch portion
22ab is formed in the tip end edge, FIG. 18c is a plan view of a spindle
portion 20a in which a through hole 23a is formed in the spindle portion
shown in FIG. 18A, FIG. 18D is a plan view of a spindle portion 20a in
which a notch portion 22ab of the tip end edge and a through hole 23a are
formed, and FIG. 18E is a plan view of a spindle portion 20a in which a
fine through hole 23a and a groove portion 17a connected thereto are
formed. In FIGS. 18B to 18E, the area of the notch portion 22ab shown in
FIG. 18B and the area of the through hole 23a or the area acquired by
adding the areas of the notch portion 22ab and the through hole 23a shown
in FIG. 18c and after that are the same. In addition, FIG. 18F is a plan
view of a spindle portion 20a in which a (bottomed) groove portion 22a is
formed along the resonator center C, and the area of the groove portion
22a is the same as the area of the notch portion 22ab shown in FIG. 18B.
Drawings of spindle portions 20a that have groove portions 22a having the
same area formed in correspondence with the through hole 23a shown in
FIGS. 18C to 18E or the notch portion 22ab and the through hole 23a will
not be presented.

[0182] The spindle portion 20a including the groove portion 22a is shown
in FIG. 18F and is a diagram used for comparing with the spindle portion
20a including the notch portion 22ab when the degree of the approach
between the frequencies of the flexural resonator and the torsional
resonator excited in the piezoelectric resonator element 1 is acquired
through a simulation.

[0183] The frequencies of the flexural resonator and the torsional
resonator excited in the piezoelectric resonator element 1 including the
spindle portion 20a shown in FIG. 18A are used as references, and the
frequencies fF and fT of the flexural resonator and the
torsional resonator and a frequency difference Δf
(=fT-fF) of each one of the piezoelectric resonator elements 1
including the spindle portions 20a shown in FIG. 18B to 18E and the
piezoelectric resonator elements 1 including the groove portions 22a
corresponding to FIG. 18F are simulated.

[0184] In the piezoelectric resonator elements 1 that include the notch
portion 22ab or the notch portion 22ab and the through hole 23a shown in
FIGS. 18B to 18E and the piezoelectric resonator elements 1 that include
the groove portions 22a having the same area corresponding to FIGS. 18B
to 18E, the changes in the frequencies fF and fT of the
flexural resonator and the torsional resonator and a frequency difference
Δf are acquired through simulations.

[0185]FIG. 19 is a diagram showing the frequencies fF and fT of
the flexural resonator and the torsional resonator excited in each one of
a piezoelectric resonator element 1, shown in FIG. 18B, including a notch
portion 22ab having the shape shown in FIG. 18B and a piezoelectric
resonator element 1, shown in FIG. 18F, including a groove portion 22a
that has the same area as that of the notch portion 22ab shown in FIG.
18B and each frequency difference Δf thereof. It is represented
that a frequency difference Δf between the frequencies of the
flexural resonator and the torsional resonator of the piezoelectric
resonator element 1 in which the notch portion 22ab is formed is smaller,
and the flexural resonator and the torsional resonator approach each
other.

[0186]FIG. 20 is a diagram showing the frequencies fF and fT of
the flexural resonator and the torsional resonator excited in each one of
a piezoelectric resonator element 1 including a through hole 23a having
the shape shown in FIG. 18c and a piezoelectric resonator element 1
including a groove portion 22a that has the same area as that of the
through hole 23a and each frequency difference Δf thereof.

[0187] It is represented that a frequency difference Δf between the
frequencies of the flexural resonator and the torsional resonator of the
piezoelectric resonator element 1 in which the through hole 23a is formed
is smaller, and the flexural resonator and the torsional resonator
approach each other.

[0188]FIG. 21 is a diagram showing the frequencies fF and fT of
the flexural resonator and the torsional resonator excited in each one of
a piezoelectric resonator element 1 including a notch portion 22ab having
the shape shown in FIG. 18D and a through hole 23a and a piezoelectric
resonator element 1 including a groove portion 22a that has the same area
as that of the notch portion 22ab and the through hole 23a and each
frequency difference Δf thereof. It is represented that a frequency
difference Δf between the frequencies of the flexural resonator and
the torsional resonator of the piezoelectric resonator element 1 in which
the notch portion 22ab and the through hole 23a are formed is smaller,
and the flexural resonator and the torsional resonator approach each
other.

[0189]FIG. 22 is a diagram showing the frequencies fF and fT of
the flexural resonator and the torsional resonator excited in each one of
a piezoelectric resonator element 1 including a fine through hole 23a
having the shape shown in FIG. 18E and a groove portion 17a connected
thereto and a piezoelectric resonator element 1 including a groove
portion 22a that has the same area as the area acquired by adding the
area of the fine through hole 23a and the area of the groove portion 17a
and each frequency difference Δf thereof. It is represented that a
frequency difference Δf between the frequencies of the flexural
resonator and the torsional resonator of the piezoelectric resonator
element 1 in which the a fine through hole 23a and a groove portion 17a
connected are formed is smaller, and the flexural resonator and the
torsional resonator approach each other.

[0190]FIG. 23 is acquired by collecting the above-described results, and
is a diagram in which the frequencies fF and fT of the flexural
resonator and the torsional resonator excited in each one of the
piezoelectric resonator elements 1 having the shapes shown in FIGS. 18B
to 18E and each frequency difference Δf thereof are represented in
correspondence with signs (b) to (e) in the horizontal axis in the
vertical axes located on the left and right sides. In the case of the
shape shown in FIG. 18B, in other words, in a case where a notch portion
22ab symmetrical with respect to the resonator center C is formed in the
spindle portion 20a, the frequency difference Δf is the smallest.

[0191]FIG. 24 is a diagram for comparing resonator leakage of a tuning
fork type piezoelectric resonator element 1 that includes only the base
portion main body 12a and resonator leakage of a tuning fork type
piezoelectric resonator element that includes a base portion 10 including
the base portion main body 12a, the connection portion 12d, and the
support arms 12b and 12c which are acquired through simulations. It is
apparent that the tuning fork type piezoelectric resonator element 1 that
includes the base portion 10 including the support arms 12b and 12c has
less resonator leakage.

[0192] As shown in the embodiment shown in FIGS. 14A and 14B, according to
the piezoelectric resonator element (tuning fork type piezoelectric
resonator element) 1 according to the embodiment of the invention, the
spindle portion is formed in the tip end portion of each vibrating arm,
and the mass portions having a heavy mass are arranged on both sides of
the resonator center in the spindle portion so as to be symmetrical.
Moreover, in each vibrating arm, the groove portions are formed on the
front and rear faces along the resonator center. By configuring as such,
the flexural resonator and the torsional resonator excited in the
piezoelectric resonator element 1 approach each other so as to be
combined together. By appropriately setting the thickness of the
piezoelectric substrate, the cutting angle, and the shapes of each mass
portion and each groove portion, the frequency-temperature
characteristics of the flexure resonator as the principal resonator of
the flexure-torsional combined resonator represent third-order
characteristics with respect to the temperature, and accordingly, there
is an advantage of acquiring the piezoelectric resonator element that has
superior temperature characteristics and has a small size.

[0193] In addition, the piezoelectric resonator element (tuning fork-type
piezoelectric resonator element) 1 acquired by rotating the cutting angle
of the piezoelectric substrate 8 around the electric axis (X axis) in the
range of 0 degree to -15 degrees, which is represented in the embodiment
shown in FIG. 14A, is configured. By setting the cutting angle as such
and appropriately setting the thickness of the piezoelectric substrate
and the like, the first-order coefficient and the second-order
coefficient of a polynomial representing the frequency-temperature
characteristics of the flexure-torsional combined resonator can be set to
approximate zero, and accordingly, there is an advantage of acquiring the
piezoelectric resonator element having superior temperature
characteristics.

[0194] As shown in the embodiment shown in FIGS. 14A and 14B, by arranging
the notch portions 22ab and 24ab that are symmetrical with respect to the
resonator center C in the center portions of the tip end edges of the
spindle portions 20a and 20b, the flexural resonator (tuning fork
resonator) and the torsional resonator excited in the piezoelectric
resonator element 1 can approach each other so as to be combined. In
addition, by appropriately setting the parameters, there is an advantage
of configuring the frequency-temperature characteristics of the flexural
resonator of the flexure-torsional combined resonator to represent
third-order characteristics.

[0195] In addition, as shown in the embodiment shown in FIG. 15, the
spindle portions 20a and 20b are reinforced by decreasing the size of the
notch portion 22ab so as to be combined with the through hole 23a,
arranging the mass portions 21 to be symmetrical with respect to the
resonator center C on both sides thereof, and arranging the bridging
portion 29a between both the mass portions 21. At the same time, the
flexural resonator (tuning fork resonator) and the torsional resonator
can approach each other so as to be combined together. Furthermore, by
appropriately setting the parameters, there is an advantage of
configuring the frequency-temperature characteristics of the flexural
resonator of the flexure-torsional combined resonator to represent
third-order characteristics.

[0196] As shown in the embodiment shown in FIG. 16, by arranging the
through hole 23a (23b) in the center portion, although the rigidity of
the spindle portions 20a and 20b increases, the change in the frequency
of the flexural resonator slightly decreases. However, by slightly
increasing the area of the through hole 23a (23b), the decrease in the
frequency can be supplemented. Also in such a case, the flexural
resonator (tuning fork resonator) and the torsional resonator can
approach each other so as to be combined together. In addition, by
appropriately setting the parameters, there is an advantage of
configuring the frequency-temperature characteristics of the flexural
resonator of the flexure-torsional combined resonator to represent
third-order characteristics.

[0197] In addition, as shown in the embodiment shown in FIG. 17, by
arranging the through hole 23a (23b) at the base portion side end of the
spindle portions 20a and 20b, although the change in the frequency of the
flexural resonator slightly decreases, by extending the groove portions
of the vibrating arms, the frequency of the torsional resonator
decreases, whereby the frequencies of the flexural resonator and the
torsional resonator approach each other so as to be combined together. In
addition, by appropriately setting the parameters, there is an advantage
of configuring the frequency-temperature characteristics of the flexural
resonator of the flexure-torsional combined resonator to represent
third-order characteristics.

[0198] Furthermore, as shown in FIG. 14A, the base portion 10 of the
piezoelectric resonator element (tuning fork type piezoelectric resonator
element) 1 includes the base portion main body 12a, the connection
portion 12d, and the support arms 12b and 12c having the "L" shape and
the reverse "L" shape, the end portions of the "L" shape and the reverse
L shape are connected, and the connection portion is configured to be
connected to the center portion of one end portion of the base portion
main body 12a through the connection portion 12d. Accordingly, the
resonator energy leaking to the support arms 12b and 12c from the
vibrating arms 15a and 15b can be reduced, and the CI value is decreased.
In addition, the impact is alleviated based on the structure of the base
portion, whereby the shock resistance is improved. As a result, there is
an advantage of acquiring the piezoelectric resonator element having no
problem of frequency variations due to a damage, a destruction, or the
like that is caused by an impact.